Two major differences to be aware of. First, weapons do not prefer to focus fire. Second, fighter movement makes combat fluid. What this means in a practical sense is that if you have a single target, it takes all the damage. If you have multiple targets, the ship being attacked isn't the only ship taking damage. Ships will fire on targets when the opportunity arises, minimizing focused fire on their primary target. A single ship or structure alone will fall much faster than one in a group. This does not hold true as often when the Borg are attacking you.
The biggest one is the Cloak. Use autocast to cloak your fleet before war, or as you retreat. Simply switch it over with your entire fleet selected, and manually cloak your Elites. To decloak, use the Fleet Decloak located on one of the Elites you have access to. If you forget and leave them on autocast, they will promptly cloak again. It's the only way to sensibly cloak and decloak large fleets in anything resembling an intelligent way. The ability AI simply can't handle the concept.
Shield restores. There are various powerful restoration methods that come with disastrous counter balancing should you use them in combat. Sadly, once again the ability AI is not the sharpest stick. You may find that these disabling or damaging abilities are better off removed from autocast until needed. They are set to avoid casting in combat, but the entry behaves like the opposite of the OnlyWhenTakingDamage casting time, so there are problematic instances where they can end up getting you killed.
The Harbinger. Boost and Draw cancel each other out. Don't go trying to use them at the same time to get both sets of bonuses, all you do is remove one with the other.
A single Galaxy Class killed my fully upgraded starbase! Why yes, yes it did! A little thinking goes a long way. The typical Elite starts out at around 200 damage per second, the typical starbase starts below 100. This 100 damage has multiple targets, so it's actually 400, but only against 4 or more targets per bank. Which brings us to the other problem. It's 25 damage per side. Unless Picard is circling your starbase, you aren't going to be doing the full 100 damage. Against a single target, even a fully upgraded starbase will be outclassed by a lone turret. The long and short of it? Just like in the shows, an unsupported starbase makes not a defended planet! They are front line logistical support, not an army unto themselves.